Verification of Machinery Salvage Value Function
Transcription
Verification of Machinery Salvage Value Function
OPEN ACCESS World J of Engineering and Pure and Applied Sci. 2011;11(3):88 ):88 Ekeocha et al al.,., 2011. 2011 Machinery Salvage Value Function Short Article Engineering ISSN 2249-0582 Verification of Machinery Salvage Value Function Rowland Jerry Okechukwu EKEOCHA, Anthony Okay ODUKWE, Jonah Chukwuemeka AGUNWAMBA ABSTRACT [ENGLISH/ANGLAIS [ENGLISH/ANGLAIS] ANGLAIS] Affiliations: Salvage value or resale value is one of the cost components of machinery replacement models. Some replacement models exclude salvage value in the build-up of cost. Yet it is the value that is adversely affected by deterioration. Various mathematical formulas for machinery salvage value have been formulated. The formula for salvage value presented by Lake and Muhlemann is of interest. It is presented in an exponential form. The suitability of this function to our industrial environment has to be justified bearing in mind that some assets have little or no secondhand value. To ensure a balanced investigation, efforts are made to obtain salvage values for motor grader, representing large scale industrial environment and photocopier, representing small and medium scale industrial environment. It is difficult to obtain salvage values because records are hardly kept for such values. However, two sets of salvage values are obtained for each of the machines. One set is for the calibration of the salvage value function by Lake and Muhlemann while the other is for comparison between the measured and predicted salvage values. This paper therefore sets out to investigate and verify the suitability of salvage value function formulated by Lake and Muhlemann to our industrial environment. It is hoped that the investigation will lead to a better understanding of the salvage value function for proper application in our industrial environment. of Mechanical Engineering, University of Nigeria, Nsukka, NIGERIA 2 Faculty of Engineering, University of Nigeria, Nsukka, NIGERIA Address for Correspondence/ Adresse pour la Correspondanc e: ekeochaj@yahoo. com Keywords: Salvage value, replacement models, verification RÉSUMÉ [FRANÇAIS/FRENCH] FRANÇAIS/FRENCH] La valeur de récupération ou de la valeur de revente est l'une des composantes du coûtdes modèles de remplacement des machines. Certains modèles de remplacementd'exclure la valeur de récupération dans l'accumulation de coûts. Pourtant, c'est la valeurqui est affectée par la détérioration. Diverses formules mathématiques pour la valeur de récupération des machines ont été formulées. La formule pour la valeur de récupérationprésentés par Lake et Muhlemann est d'un intérêt. Il est présenté dans une forme exponentielle. La pertinence de cette fonction pour notre environnement industriel doit êtrejustifié portant à l'esprit que certains actifs ont peu ou pas de valeur d'occasion. Afin de garantir une enquête équilibrée, des efforts sont déployés pour obtenir des valeurs de récupération pour les niveleuses, représentant l'environnement industriel à grande échelleet d'un photocopieur, représentant les petites et moyennes environnement à l'échelle industrielle. Il est difficile d'obtenir des valeurs de récupération parce que les dossiers ne sont guère conservés pour de telles valeurs. Cependant, deux ensembles de valeurs de récupération sont obtenus pour chacune des machines. Un ensemble est pour le calibrage de la fonction de valeur de récupération par le lac et les Muhlemann tandis que l'autre est pour la comparaison entre les valeurs de récupération mesurés et prédits. Ce document vise donc à enquêter et de vérifier l'adéquation de la fonction valeur de récupération formulée par Lake et Muhlemann à notre environnement industriel. Il est à espérer que l'enquête va conduire à une meilleure compréhension de la fonction de valeur de récupération pour une application correcte de notre environnement industriel. Mots-clés: La valeur de récupération, des modèles de remplacement, la vérification. INTRODUCTION 1 Department Accepted/Accepté : November, 2011 Citation: Ekeocha RJO, Odukwe AO, Agunwamba JC. Verification of Machinery Salvage Value Function. World Journal of Engineering and Pure and Applied Sciences 2011;1(2):88-90. service or economic life especially where an active resale Salvage value refers to the proceeds from the sale of market does not exist. Records are not usually kept for second hand plant/machine. It depends on the the scrap values and no value is usually placed on the conditions of the plant/machine at the point of sale. Such cannibalized parts of such machinery. A way of conditions include deterioration, the service life (man- predicting salvage value for machinery replacement hour), maintenance history and the capacity of the models has to be sought. Various mathematical formulas plant/machine. Records for salvage values of machinery for machinery salvage value have been presented [1-3]. are not easy to achieve when compared to records for the Lake and Muhlemann [4] formulated a salvage value cost prices of similar machinery. Most machinery and function that is in exponential form. There is therefore equipment are scrapped or cannibalized after their the need to verify the suitability of the function to our OPEN ACCESS © Research | Reviews | Publications, 2011 http://www.rrpjournals.com/ ISSN 2249-0582 World J of Engineering and Pure and Applied Sci. 2011;11(3):89 ):89 Ekeocha et al., al., 2011. 2011 Machinery Salvage Value Function OPEN ACCESS industrial environment since it is one of the cost value of the correlation coefficient between the measured components in most machinery replacement models. and the predicted salvage values gives an indication of The objective of this paper is to verify the suitability of the suitability of the salvage value function to our salvage value function by Lake and Muhlemann [4] to industrial environment. our industrial environment. IMPLEMENTATION METHODOLOGY The salvage value function by Lake and Muhlemann [4] The methodology is a combination of analytical and is given by experimental processes. The processes begin with the collection of two sets each of measured (actual) salvage Where S(t) = Salvage Value values for CAT 140H Motor Grader and SHARP SF-2035 Q = Cost of Machine Photocopier (Field Data) followed by the calibration of d = Deterioration the salvage value function using a set of the field data to t = Time (age) obtain values for deterioration. The next step is to use the calibrated salvage value function to predict salvage CALIBRATION OF THE FUNCTION values for the Motor Grader and Photocopier. Another The regression line [5] is given by set of field data is then used to plot separate graphs of measured and predicted salvage values of the machines for comparison. Finally the correlation coefficients And the slope of the regression line is given by between the measured and predicted salvage values of the Grader and Photocopier are derived to ascertain the strength and linear dependence of the two variables. The Table 1: This Table shows variation of salvage value with Age of Motor Grader and Photocopier t 2 3 4 5 6 7 8 9 10 11 12 13 S(t)g 248500 230000 210000 194000 163500 161000 155250 161000 137500 104500 105000 98500 S(t)p 145000 135000 120000 115000 100000 95000 90000 85000 84000 S(t)g = Salvage Value of the Grader in Dollars; S(t)p = Salvage Value of the Photocopier in Naira; t = Age in Years Source: Resale market (Grader), Business centre (Photocopier)[6] Table 2: This Table shows variation of Measured and Predicted Salvage Values S(t) with Age of Motor Grader and Photocopier Age t Measured Salvage Value of the Motor Grader Predicted Salvage Value of the Motor Grader 1 Measured Salvage Value of the Photocopier Predicted Salvage Value of the Photocopier 140000 142935 2 264500 258683 130000 136203 3 227750 237396 120000 129788 4 214000 218854 110000 123675 5 184750 201302 100000 117850 6 158750 185157 90000 112299 7 152000 170307 80000 107010 8 147250 156649 75000 101969 9 161000 144086 60000 97167 10 109500 132530 11 104500 121901 12 105000 112125 13 94250 103132 © Research | Reviews | Publications, 2011 http://www.rrpjournals.com/ OPEN ACCESS ISSN 2249-0582 World J of Engineering and Pure and Applied Sci. 2011;11(3):90 ):90 Ekeocha et al., al., 2011. 2011 Machinery Salvage Value Function OPEN ACCESS Applying the least square method on the data in Table 1, suitable for application in the small and medium scale b = - 0.0363 and d = 0.0802 for the Grader industrial environment. It is of interest to note that both b = -0.02096 and d = 0.0471 for the Photocopier the Grader and Photocopier have remarkable secondhand value (Tables 1 and 2). The percentage Q = $305760 for the Grader and N150000 for the deviation between the measured and predicted salvage Photocopier values is generally low with absolute values ranging from 2.22 to 17.38% for the Grader and 2.05 to 38.25% for Figure 1: This figure shows comparison of the measured the Photocopier. and predicted salvage values of grader CONCLUSION The measured and predicted salvage values are positively correlated with correlation coefficient of 0.98 for the Grader and unity for the Photocopier. The salvage value function by Lake and Muhlemann [4] is therefore suitable to our industrial environment. The remarkable secondhand value of both machines is worthy of note. The generally low absolute values of the percentage deviation between the measured and predicted salvage values of both the Grader and Photocopier is another indication of the suitability of the salvage value function to our industrial environment. REFERENCES Figure 1: This figure shows comparison of the measured [1] Arora SR, Lele PT. A note on optimal maintenance policy and sale date of a machine, Management and predicted salvage values of photocopier Science, 1970, vol.17, no.3, p.170-3. [2] Glassier GJ. The age replacement Technometrics, 1967, vol.9, problem, p.89-91. [3] Kamien NL, Schwartz MI. Optimal maintenance and sale age for a machine subject to failure, Management Science, 1971, vol.17B, p.495-504. [4] Lake DH, Muhlemann AP. An equipment replacement problem, Journal of operational society, 1979, vol.30, p.405-11. [5] Ekeocha RJO. Dynamic modeling of machinery replacement problems, a thesis for the award of DISCUSSION doctorate degree in the department of mechanical The measured and predicted salvage values of the Motor engineering, University of Nigeria, Nsukka, 2011. Grader are linearly dependent with a correlation [6] Machinery resale market, Abuja for the Grader and coefficient of 0.98 (figure 1). This is an indication of the Business centres Abuja, Nigeria for the photocopier, suitability of the salvage value function by Lake and 2011. Muhlemann [4] to the large scale industrial environment. The measured and predicted salvage values of the ACKNOWLEDGEMENT / SOURCE OF SUPPORT Photocopier Nil also show a high degree of linear dependence of the two variables with a correlation coefficient of unity (figure 2). This means that the salvage CONFLICT OF INTEREST value function by Lake and Muhlemann [4] is very No conflict of interests was declared by authors. © Research | Reviews | Publications, 2011 http://www.rrpjournals.com/ OPEN ACCESS